a) \(\left(\dfrac{3}{8}-\dfrac{1}{5}-\dfrac{1}{3}\right)+\left(\dfrac{5}{8}-1\dfrac{3}{7}-\dfrac{4}{7}\right)+\dfrac{1}{3}\)
\(=\dfrac{3}{8}-\dfrac{1}{5}-\dfrac{1}{3}+\dfrac{5}{8}-\dfrac{10}{7}-\dfrac{4}{7}+\dfrac{1}{3}\)
\(=\left(\dfrac{3}{8}+\dfrac{5}{8}\right)+\left(\dfrac{-1}{3}+\dfrac{1}{3}\right)+\left(\dfrac{-10}{7}-\dfrac{4}{7}\right)-\dfrac{1}{5}\)
\(=1+0+\left(-2\right)-\dfrac{1}{5}\)
\(=-1-\dfrac{1}{5}\)
\(=\dfrac{-6}{5}\)
b) \(-24.\left(\dfrac{1}{3}-\dfrac{1}{4}\right)^2-1,5\)
\(=-24.\left(\dfrac{1}{12}\right)^2-\dfrac{3}{2}\)
\(=-24.\dfrac{1}{144}-\dfrac{3}{2}\)
\(=\dfrac{-1}{6}-\dfrac{3}{2}=\dfrac{-1}{6}-\dfrac{9}{6}=\dfrac{-10}{6}=\dfrac{-5}{3}\)
c) \(2^2-\left(-\dfrac{5}{7}\right)^0+\left(\dfrac{1}{3}\right)^4.3^6\)
\(=4-1+\dfrac{1}{81}.729\)
\(=4-1+9\)
\(=3+9=12\)
d) \(23\dfrac{1}{3}:\left(\dfrac{-5}{7}\right)+13\dfrac{1}{3}:\dfrac{5}{7}\)
\(=\dfrac{-70}{3}.\dfrac{7}{5}+\dfrac{40}{3}.\dfrac{7}{5}\)
\(=\dfrac{7}{5}\left(\dfrac{-70}{3}-\dfrac{40}{3}\right)\)
\(=\dfrac{7}{5}.\left(-10\right)\)
\(=-14\)
e) \(\dfrac{3}{4}.\dfrac{8}{5}+\dfrac{6}{15}:\dfrac{4}{3}-1\dfrac{2}{5}:1\dfrac{1}{3}\)
\(=\dfrac{3}{4}.\dfrac{8}{5}+\dfrac{6}{15}.\dfrac{3}{4}-\dfrac{7}{5}.\dfrac{3}{4}\)
\(=\dfrac{3}{4}\left(\dfrac{8}{5}+\dfrac{6}{15}-\dfrac{7}{5}\right)\)
\(=\dfrac{3}{4}\left(\dfrac{24}{15}+\dfrac{6}{15}-\dfrac{21}{15}\right)\)
\(=\dfrac{3}{4}.\dfrac{9}{15}\)
\(=\dfrac{9}{20}\)
